Chemistry Reference
In-Depth Information
temperature the
partial molar free energy due to the solute-solvent interaction is assumed to be zero and deviations
from ideality (ideal solution) become zero. What this means is that as the temperature of the solution
of a polymer approaches
In addition,
Flory temperature,
Y
is treated as a parameter,
Y ¼ k
1
T
/
C
1
At
Y
, the solvent becomes increasingly poorer and the excluded volume effect
becomes smaller and approaches zero with the molecules interpenetrating one another with zero net
interaction. The solvent is referred to as a
Y
temperature the polymer molecules
attract each other, the excluded volume is negative, and the polymer precipitates. This can be
expressed as [
63
]:
Y
, solvent. Below
Y
C
1
k
1
¼ C
1
ð
Y=TÞ¼
:
x
1
1
0
5
When the chains are extended, their conformations may be considered as being determined by
equilibrium between the forces of expansion due to excluded volume and the forces of contraction
due to chain segments expanding into less probable conformations. Based on random flight statistics,
the chains are extended linearly by a factor
a
over their dimensions. The actual root-mean-square end-
R
0
2
)
0.5
. The change in the elastic part of free energy is
to-end distance is equal to
a
(
2
2
DF
el
¼ kT½
1
:
5
ða
1
Þ
ln
a
where the parameter
a
can be expressed in terms of thermodynamic quantities:
5
3
0
:
5
a
a
¼
2
C
m
C
1
ð
1
Y=TÞM
In the above equation,
C
m
represents a combination of molecular and numerical constants. Based
on the above equation, at
1. It has been stated that the Flory-Krigbaum treatment
must be treated with some reservations, because it predicts that
Y
temperature
a ¼
a
increases without limit with
increasing molecular weight [
63
].
2.7 Molecular Weights and Molecular Weight Determinations
The physical properties of polymers are also related to their molecular weights. Melt viscosity, hot
strength, solvent resistance, and overall toughness increase with molecular size. Table
2.4
illustrates
the effect of molecular weights (size) upon physical properties of polyethylene [
64
].
2.7.1 Molecular Weight Averages
Random events govern the process of synthetic polymer formation, whether it is by a chain propagating
process or by a step-growth reaction. The result is that the chains vary in lengths. (There are special
methods available, however, in chain-growth polymerizations that lead to formation of polymer
molecules that are almost equal in length. This is discussed in subsequent chapters) As a result, most
polymeric materials cannot be characterized by a single molecular weight, but instead must be
represented by statistical averages [
64
]. These averages can be expressed in several ways. One way
is to present an average as a
number average
molecular weight. It is the sum of all the molecular
weights of the individual molecules present divided by their total number. Each molecule contributes
equally to the average and can be obtained by averaging the measurements of all the colligative
properties. If the total number of moles is
N
i
, the sum of these molecules present can be expressed
as,
SN
i
. The total weight
o
of a sample is similarly the sum of the weights of all the molecular
species present
